This one is even weirder to me. If it is best effort then this means that it is okay if the work doesn't get done. If that is the case, then why can't it be done the next morning?

My team has an "oncall" shift like this where we assign a person to be responsible for triaging bugs and other non-urgent alerts just so we don't all stare at it and wait for somebody else (or inevitably me, the lead) to handle it but they are explicitly told that this responsibility does not extend beyond working hours.